The velocity potential and the interacting force for two spheres moving perpendicularly to the line joining their centers Authors L. Li Department of Mechanical Engineering University of Michigan W. W. Schultz Department of Mechanical Engineering University of Michigan H. MerteJr. Department of Mechanical Engineering University of Michigan Article

Received: 25 September 1991 Accepted: 20 July 1992 DOI :
10.1007/BF00127479

Cite this article as: Li, L., Schultz, W.W. & Merte, H. J Eng Math (1993) 27: 147. doi:10.1007/BF00127479
Abstract The velocity potential around two spheres moving perpendicularly to the line joining their centers is given by a series of spherical harmonics. The appropriateness of the truncation is evaluated by determining the residual normal surface velocity on the spheres. In evaluating the residual normal velocity, a recursive procedure is constructed to evaluate the spherical harmonics to reduce computational effort and truncation error as compared to direct transformation or numerical integration. We estimate the lift force coefficient for touching spheres to be 0.577771, compared to the most accurate earlier estimate of 0.51435 by Miloh (1977).

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© Kluwer Academic Publishers 1993